Method of and means for recording line drawings on the screen of a cathode ray tube under computer control

ABSTRACT

Curves are plotted and displayed on the screen of a cathode ray tube by deriving control voltages from the differences between the coordinates of adjacent points of a curve, controlling the plotting of line portions with the derived voltages, maintaining the speed and current of the recording electron beam of the CRT constant and maintaining a uniform brightness of the several portions of a trace.

lJ'nited States alt 1191 Redecker et a1,

1451 ,luly 17,1973

[ METHOD OF AND MEANS FOR RECORDING LINE DRAWINGS ON THE SCREEN OF ACATHODE RAY TUBE UNDER COMPUTER CONTROL [75] Inventors: FriedrichRedecker, Kiel; Ruediger Sommer, Raisdorf, both of Germany [73]Assignee: Dr.-Ing. Rudolf Hell, Kiel, Germany [22] Filed: July 15, 1970[21] Appl. No.: 54,938

[30] Foreign Application Priority Data July 16, 1969 Germany P 19 36051.1

[52] US. Cl 315/26, 235/6l.7, 340/324 A [51] Int. Cl. ll-l0lj 29/72 [58]Field of Search 315/26, 21 R, 21 MR, 315/18, 22, 24; 235/61, 61.7, 61PK, 61.11 G;

[56] References Cited UNITED STATES PATENTS 3,252,045 5/1966 Griffin340/324 A 3,430,207 2/1969 Davis 340/324 A X 3,434,135 3/1969 Granberget a1 315/18 X 3,488,483 1/1970 Freedman 340/324 A X 3,482,309 12/1969Bouchard 315/22 3,320,409 5/1967 Larrowe 340/324 A 3,333,147 7/1967Henderson 340/324 A X 3,459,926 8/1969 Heilweil et a1....... 340/324 A X3,473,079 10/1969 Adometto et. a1. 315/22 3,510,865 5/1970 Callahan eta1 340/324 A Primary Examiner-Carl D. Quarforth Assistant ExaminerE. E.Lehmann Attorney-Hill, Sherman, Meroni, Gross & Simpson [57] ABSTRACTCurves are plotted and displayed on the screen of a cathode ray tube byderiving control voltages from the differences between the coordinatesof adjacent points ofa curve, controlling the plotting of line portionswith the derived voltages, maintaining the speed and current of therecording electron beam of the CRT constant and maintaining a uniformbrightness of the several portions of a trace.

6 Claims, 10 Drawing; Figures Pat en te d July 17, 1973 7 Sheets-Sheet lPatented July 17, 1973 3,746,912

7 Sheets-Sheet 5 INV/ am 01 Friedrich Redecker I I, RUed/ger SommerPatented July 17, 1973 7 Sheets-Sheet 4 axis Patented July '17, 1973 7Sheets-Sheet 5 III'IIIIIIIIIIIIII /.w\-'/:.\"/-/ Friedrich Redecke'r RLiedigler Sommer Patented July 17, 1973 I 3,746,912

"1v Sheets-Sheet 6 a m l) 2 o R [L m V/QN/ 01, Friedrich RedeckerRu'ediger Sommer Patent ed July 17, 1973 7 Sheets-Sheet 7 v1 I uFriedrich Redecker Riiedig'er Sommer METHOD OF AND MEANS FOR RECORDINGLINE DRAWINGS ON THE SCREEN OF A (IATll-IODE RAY TUBE UNDER COMPUTERCONTROL BACKGROUND OF THE INVENTION 1. Field of the Invention Thepresent invention relates to a method of and means for recording linedrawings on the screen of a cathode ray tube under computer control, thecoordinates of individual points on the lines of the drawings beingspaced at differing intervals and continuous line series beingrepresented by straight lines connecting these points, said linesapproximating the line drawing.

2. Description of the Prior Art Cathode ray tubes are frequently used todisplay information calculated by a computer. Such illustrations aregenerally constructed from a limited number of symbols, i.e., numbers,letters and characters, whose recording data are distributed in anelectronic memory of the recording apparatus or in the computer. Thesedata consist of binary numbers of coordinates for positioning on thescreen of the cathode ray tube and of binary coded numbers givingdetails of the length pieces of the individual picture lines from whichthe symbols are constructed. Each picture line piece is built up from awhole multiple of a minimum piece whose size is barely preceivable bythe eye. The symbols thus have a raster structure. The data from thesymbols are distributed under certain addresses in the memories. Uponcall-up of this address they control, by means of the computer, therecording of the symbols on the screen of the cathode ray tube.

Often it is desired to plot not only symbols but also so-called linedrawings, i.e. drawings that are made up of continuous series of linesof the same line thickness and shape. For example, a weather map can beused which, in addition to the symbols and meteorological signs, alsocontain continuous series of lines of varying shapes, i.e., coastlinesand iso-lines. Apparatus which plot weather maps are referred toasplotters. Also during scientific computer calculations, functionsoften result which can be advantageously recorded with the aid of theplotter so that they are directly visible as curves and can bephotographically fixed for evaluation.

The plotting of such curves can be particularly simply effected byplotting rows of points close to one another so that the eye observes acontinuous solid line. Plotting of this kind has the disadvantage that alarge number of points have to be displayed on the screen of the cathoderay tube. Each point has to be determined by an X- and a Y-coordinatewhich, in turn, have to be determined in a .plurality of individualcalculations and possibly stored in some form of memory.

In order to decrease this large amount of data, in an improved method ofplotting, small lines of fixed length are employed instead of points. Adefinite number of line units having various angles of inclination isfixed. By lining up a plurality of these lines of appropriateinclination in any series and amount, approximation to the requiredcurve can be attained.

However, it has been obligatory to compromise in the case oflineplotting. If the continuous series oflines has to be plotted with fewline units of greater length, then less information and storage room isnecessary, however, a rectangular, rugged and unpleasant series of lineswas obtained. If the lines are, however, sufficiently small to overcomethis disadvantage, then the amount of data which has to be plotted,addressed and stored increases proportionally.

In an advantageous method of recording, as small as possible a number ofpoints on the continuous series of lines is determined, at differentlysized and advantageously chosen spacings, and these points are connectedto one another by straight line portions. This gives rise to a polygonaltrace approximating the actual curve required. In order to achieve asgood as possible an approximation, many points must be laid downclose toone another in curved pieces having small radii of curvature, fewerpoints being necessary in curved pieces having a large radius ofcurvature and in straight members, and these need be provided only onthe periphery and end. The line drawings thus produced have a smootheffect despite the enormously varying spacing between the points makingup these lines. with a relative small number of points they satisfy therequirements for accuracy and satisfy the requirements to take up aslittle data and storage space as possible.

One improtant requirement is, however, not fulfilled. The line thicknessmust be uniform over the total length of the line series, if the latteris to have a satisfactory appearance. It is very difficult to achievesuch uniformity, due to the vary great difference in length of the partpieces, and the recording times, so that uniform illumination is notachieved and thus there is no equality in the line thickness. Two faltsarise: firstly, the speed and brightness of the scanning point is notconstant between the points delineating the line so that line piecesappear as commas, i.e., thicker to one side; and secondly, thebrightness of the total line series is also not uniform due to thevarying basic brightness of the individual line pieces. Therefore, theappearance of the line series is poor.

SUMMARY OF THE INVENTION The straight union a of two points on the curvedetermined by the coordinates x ;y and x ;y is:

2 l) (y2 yl) V Y The electron beam has to move over this path a duringplotting of the curved piece. In order to achieve equally brightrecording of the whole line series, each individual piece of the tracemust be recorded at constant speed and beam intensity, and the beamintensity must be such that a uniform brightness is attained.

To this end, and according to the invention, voltages are derived fromthe differences between the coordinates of adjacent points and thesevoltages are fed to control means operative during plotting ofindividual line pieces, to keep the speed and current of the recordingelectron beam constant, and during the plotting of all the line members,to achieve uniform brightness on the screen of the recording tube.

BRIEF DESCRIPTION OF THE DRAWINGS Other objects, features and advantagesof the invention, its organization, construction and operation will bebest understood from the following detailed description, taken inconjunction with the accompanying drawings which show some embodimentsof the invention by way of example, and in which:

FIG. 1 shows a polygon, which is approximated to a curved path;

FIG. 2 shows a circuit diagram of a first proposal providing a uniformand constant speed and constantcurrent of the electron beam for all theline pieces;

F IGS.3 and 4 show graphical illustrations for developing the followingcircuit arrangement of FIG.

FIG. 5 shows a circuit diagram of a second proposal providing constantspeed and constant electron beam current;

FIG. 6 shows a circuit diagram of a first proposal for recording linepieces of different length in equal times and at controlled speed andbeam current;

FIG. 7 shows a graphical illustration for an approximation method forsolving the problem referred to in connection with the circuit of FIG.6;

FIG. 8 shows a circuit diagram for carrying out the approximation methodof FIG. 7;

FIG. 9 shows graphical illustrations for a further method according toFIG. 7; and

FIG. shows a circuit diagram for carrying out the further approximationmethod of FIG. 9.

DESCRIPTION OF THE PREFERRED EMBODIMENT The plotting of anyrepresentations on the screen of a cathode ray tube is conventionallycarried out by de flecting an electron beam, focussed to a point, in twoorthogonal coordinate directions and preferably horizontally(Jr-direction) and vertically (y-direction), and at the same time thebeam intensity is appropriately controlled. By establishing a pair ofcoordinates x and y, the position of a point on the screen is determinedand can be controlled by deflection currents or voltages which areallocated to these coordinates.

If a definite point on the screen is to be controlled by a computer ormemory, then this is achieved by the numerical values of the coordinatesx and y of the point, which are offered in binary numbers depends on thedegree of resolution which the electron beam point is to attain on thescreen. The following numbers are of interest as a practical example.The usable diameter of this screen should amount to approximately 210mm. so that a square field of 150 mm, can be used. The electron beampoint should have a diameter of 0.05 mm. Then for instance 3,000positions are possible in each coordinate direction, in the whole field9 X 10. For detailing the position of, or expressed in data techniqueparlance, addressing a point in the field, a twelvedigit binary numberis required for x and y.

Referring now to the drawings, FIG. 1 represents any curved path whichis to be plotted on the screen.

' In order to be able to use as little control data as possible, a fewpoints P,, P, P,, are selected on the curved path. The spaces are ofdifferent sizes and chosen so that straight connecting pieces betweenadjacent points (shown dashed) offer as good as possible anapproximation to the real curve.

The curved piece P, P, is determined by the coordinates x,;y, for pointP, and x,;y, for point P In order visibly to plot the connecting line P,P,, the electron beam must follow the path from P, P, at a finite speedand a fixed constant brightness.

The path which the beam is to take is the hypotenuse of the right-angledtriangle having the short sides Ax and Ay, wherein: Ax x x, and Ay y 31y,.

In order to move the electron beam along the straight path a uniformlyfrom P, to P,, the deflection voltages for both the coordinates mustchange uniformly at the same time from x, to x, or from y, to y With aconstant electron beam current, the line portion is recorded at an evenbrightness.

The line portions P P P P, ...(P,, l) P,,, succeed the line portion P, PThey form a continuous line which adapts itself closely to the curvedpath. So that the whole continuous line shall have an even linethickness, the individual line portions must be recorded at an evenbrightness. If the concession is made that large line pieces be recordedat the same speed as small ones, then the point brightness will also beequal for all the line pieces and the whole line series is evenlyrecorded. Corresponding to a second proposed solution the time forrecording the individual line portions is to be equal. From the criteriaof constant time intervals, which are given by a timing pulse generator,the control values for the beam speed and current can be derived by thedistance between two points determined by the differences in thecoordinates.

For implementing the first of the alternatives the following equation isto be fulfilled:

V R V A): +Ay constant ps V signifying speed, and R a normal size, bywhich a constant real speed is adjusted.

FIG. 2 shows a circuit diagram of an electronic arrangement with whoseassistance the above function of expression a is simulated. The circuitdesign implements the function obtained by squaring the expression V R2.M R. Ay

It is assumed that the differences Ax and Ay of the x and y coordinatesof both the points between which the curved portion is recorded havealready been calculated and are available as proportionaldifferenceivoltages, 5x and 8 y. These difference voltages reach inputterminals 1 and 2 of the circuit arrangement. Firstly, they passvariable gain amplifiers 3 and 4 without change and, via circuitconnections 5 and 6, arrive at function amplifiers 7 and 8 which squarethe voltages according to the equation b. The output voltages atconductors 9 and 10 are added in an adder ll, simultaneously comparedwith a control voltage supplied via line 12 It originates from acontrollable voltage source 13 and represents the value V. The voltagesimultaneously amplified and obtained in the adder 11 passes over a line14 simultaneously to the control inputs of the variable gain amplifiers3 and 4 and so regulates these latter that in the regulating system theadjusted and regulated values are equal to one another.

The voltages appearing in lines 5 and-6 control a sawtooth generator 16for horizontal deflection and a sawtooth generator 26 for verticaldeflections, in such a manner that voltages arise in lines 17 and 18,whose differential quotient is proportional to the control voltages inlines 5 and 6. These voltages pass via adders l9 and 20 to deflectioncoils 21 of a cathode ray tube 22 and effect movement of the electronbeam from one point P to its adjacent point P, The movement thereforeemanates from a basic position which is determined by the coordinates ofthe point P namely x(P,) and y(P,). Voltages corresponding to thesecoordinate values pass via lines 23 and 24 to second inputs of theadders l9 and and determine the initial position for the movement of theelectron beam. The adders 19 and 20 in the example shown alsosimultaneously transform the controlling voltages into deflectingcurrents. The brightness of the electron beam is adjusted to a desiredvalue by means of an adjustable voltage source and the deflection timeof the individual saw-tooth phases is proportional to the line portionsto be recorded. A suitable switch (not shown) is provided for thispurpose.

A second solution of the object of recording line series at a constantrecording speed and constant brightness is shown in FIG. 5. Thisarrangement avoids electronic control (feedback) loops and is thereforefree from any tendency to set up interfering control oscillations. Thecircuit design is modeled on the equation a as in the aforementionedexample.

In the triangle formed in FIG. 3 from Ax and Ay, Ay/Ax is the tangent ofthe angle formed by Ax and 2 V 7x y (b arc tg Ay/Ax The speed at whichthe electron beam moves in the x-direction is:

t.) s cos 4 are e y/ xl and in the y-direction:

V V, sin (b =(sin arc tg Ay/AxlV,

V being the desired constant beam speed in the reproducing direction S.

Both the functions can be simulated electronically. It is, however,advantageous to limit the range of the variables Ay/Ax to be used to theregion between 0 and 1, because the functions in this interval areapproximately rectilinear and can be simulated electronically moreeasily than in the total area from 1 to The range Ay/Ax l is considered,cos arc tgAy/Ax being replaced by sin arc tg Ax/Ay and sin arc tgAy/Axbeing replaced by cos are tgAx/Ay.

FIG. 4 shows in the two curves 26 and 27, the functions sin arc tgAy/Axand cos are tgAy/Ax. In the range from 0 to 1, sin arc tg increases fromthe point 28 along the branch of the curve 26 to point 29. One point,e.g., 30 on the branch of the curve in the region of 1 to w correspondsto the point 30' of the curve 27 for the range 1 to 0. The whole branchof the curve 26 in the range of 1 to m can be replaced by the branch 27in the range of l to 0 between point 29 and 32. The same also appliesinversely. The point 311 on the branch of the curve 27 in the range of lto 00 corresponds to point 31 on the branch 26 in the range of l to 0between the points 29 and 28. The functions sin are tg Ay/Ax aretherefore replaced by cos arc lg Ax/Ay and cos arc tg Ay/Ax are replacedby sin arc tgAx/Ay when sin arc tg Ay/Ax is greater than cos arc tgAy/Ax so the branches of the curve are avoided in the range of l toshown hatched.

This exchange of functions in the electronic production of the proposedsolution occurs after comparison in size between Ax and Ay by simpleswitching.

FIG. 5 shows a suitable circuit. arrangement to accomplish the foregoingproposal. The difference volt ages 8x and 8y pass from the inputterminals 1 and 2 simultaneously to a comparator 33 and a switch 34. If8x 8 y, the switch 34 remains in the position shown. The voltage 8x isapplied to a line 36 and the voltage by to a line 37. If, however, 815y, the switch 34 is reversed. The voltage 6y reaches the line 36 andthe voltage 8x the line 37. The voltage on the line 36 is thereforealways smaller than that on the line 37.

A dividing circuit 38 divides the voltage at its one input 36 by thevoltage applied to its other input 37. The quotient voltage on theoutput line 39 is simultaneously fed to two function generators 40 and41. The function generator 40 forms the function sin are tg and thefunction generator 41 the function cos arc tg. The output voltage onlines 42 and 43 control the saw-tooth generators 44 and 45 which supplythe currents for deflection of the electron beam in the cathode raytube. The deflection currents are, however, fed through a switch 48which is simultaneously with and similarly to the switch 34, controlledby the comparator 33 via line 35. If, therefore, 8x 8y, then theconnection shown exists, and the deflection current passes through aline 47 to a terminal of the deflection coils for horizontal deflection.Thus, the current controls the vertical deflection via a terminal 49through a line 46. The horizontal deflection follows the function cosarc lg and the vertical deflection the function sin arc tg.

If 8x 8y, the comparator 33 responds and actuates the switches 34 and48. As a result, 1 is connected to 37 and 2 to 36 at the input,furthermore 46 is connected to 50 and 47 to 49. The horizontaldeflection now follows the function sin arc tg and the verticaldeflection the function cos arc tg.

For adjusting a desired brightness of the electron beam an adjustablevoltage source 25 is also used in this case. A basic positioning isrequired, which details the initial point during the recording of eachline member. These basic deflection currents have the same function asis described in FIG. 2 and was shown at the lines 23 and 24 and aremixed with the deflection currents in the lines 49 and 50.Re-representation is therefore in this case unnecessary.

The switches 34 and 48 shown in the drawings as mechanical contacts forcase of illustration, are actually constructed from logic componentsincluding diodes or transistors.

The second alternative solution of the invention consists in plottingthe connecting lines between adjacent points always in the same time.This solution has the result that the recording speed differs verygreatly and the brightness of the light spot i.e:., the intensity of theelectron beam has tobe controlled so that all the line pieces areplotted equally brightly or approximately equally brightly. The beamcurrent I is therefore dependent upon the deflection speed:

where E is an adjustment constant and flin a function for correcting thenon-linearity between control voltage and beam current as well asbetween beam current and spot brightness on the screen.

Simulation of the function fis made possible with the aid of thearrangement shown in FIG. 6. The difference voltages 8x and By areapplied to the terminals 1 and 2 and pass to function generators 53 and54, which form the squares 8x and 8y? The resultant voltages on lines 55and 56 are added by means of adder 57, and the square root is extractedfrom the total be means of a function generator 59 so that at the outputfrom a line 60 there is roduced a voltage proportional to the size V 8):8y This voltage is to control the beam current of the cathode ray tube22 and therefore the brightness of the light spot to be plotted. In thisway, proportionality remains guaranteed. The control voltage ispredistorted by the correcting member 61 f in such a manner thatnon-linear distortions are compensated between the control voltage andbeam current, as well as between beam current and light intensity of thetube. The pre-distorted voltage passes via a line 62 to the controlelectrode of the tube.

Simultaneous with the function generators 53 and 54, saw-toothgenerators 63 and 64 are controlled by 8x and 8y. The slopes of thesaw-tooth currents supplied to lines 67 and 68 are proportional to thevoltages 8x or 8y. A timing pulse generator 65 supplies startandstop-pulses at regularly equal intervals simultaneously to both thedeflection amplifiers over a line 66. During each interval, a line pieceis plotted between two adjacent points. The deflection currents for thebasic position are also added in this case in the manner alreadydescribed, to lines 67 and 68.

This aforementioned proposal can lead to technical difficulties in casesat the limits. If the ratio between the maximum and minimum possiblebeam speed is very great then it is difficult to simulate the expressionf with sufficient precision. When electronically squaring andsubsequently forming the square root, considerable errors can occurmoreparticularly at low beam speeds. The following proposal avoids thesecalculation operations by using an approximation method. It offers,using only additative calculation operations and with minimalelectronics, a sufficiently satisfactory result. The following reasonslead to the new solution.

I tshould be in the following all expressions Ax, Ay, x and 6y areabsolute values that means their signs are always positive. The constantF is attributed to the value l/VE for standardizing the calculation.With a constant Ay, Ax increases from 0 to Ax=Ay. V then follows thepath shown in FIG. 7 at curve 70. Its smallest value is Ay/\/ E 0.7Ay atAx=0. its greatest Ay at Ax=Ay. The curve 70 is applicable for any valuefrom Ax and Ay, Ax and Ay being interchangeable.

A straight line 71 is laid through the curve 70 in such a manner that asgood as possible approximation to the curve 70 is achieved. For example,the straight line 71 is located by the point Ax Ay 1. It intersects theordinate at 0.68.

The straight line 71 can be obtained by adding straight lines 72 and 73.The straight line 72 is represented by the equation:

A r (Ax Ay) (h) whereby r 0.5, and the straight line 73 by the equation:

B r I Ax Ay I where r is equal to the amount r enclosed on the ordinatebetween the straight lines 71 and 72, namely -0.l8.

The electronic execution of the addition of both the equations h and iis shown in the circuit arrangement according to FIG. 8.

The difference voltages 6x and 8y are applied to the inputs 1 and 2. 6xis simultaneously fed to a first input of an adder 74, a subtractor andthe saw-tooth generator 63 for horizontal deflection, and 8y is fed tothe second input of the adder 74 and the subtractor 75 as well as to thesaw-tooth generator 64 for vertical deflection. In the device 74 asimple adder, the total 6x 5y is formed and fed to an adding device 77.The difference 6x 8y is formed in the substractor 75, and is passed viaa line 78, a rectifier 79 and a conductor 80 to the second input of theadder 77. The rectifier 79 is provided to make the difference 8x 8yeffective according to their amount.

Correction of the non-linearity between the control voltage andbrightness of the cathode ray tube occurs, as already described, withthe aid of the correction amplifier 61. The saw-tooth generators 63' and64 supply the current for the horizontal and vertical deflection vialines 67 and 68. They are, as already explained in the description ofFIG. 6, steadily increasing (or falling) currents, whose rates of changedI/dt are proportional to 8x or By. The timing pulse generator 65supplies startand stoppulses to the saw-tooth generator at regularlyequal intervals via line 66. During each interval, one line piece isplotted between two adjacent points.

The approximation achieved with the straight line 71 is sufficient inmany cases because it is controlled according to the brightness of theelectron beam, and the eye is not very sensitive to depth or widthdeviations of the lines recorded. Nevertheless a requirement for betterapproximation to the real curve 70 can be fulfilled. Instead of thestraight line 71, a continuous line is produced from two to more smallerstraight pieces which adapt themselves as a polygonal path to the realcurve with increasing exactitude as the number of pieces increases.

FIG. 9 shows the improvement when using two straight pieces, namely 81and 82. The knee 83 at which the members meet, is located for example atAx The line series 81/82 is, as apparent from the drawing, obtained bythe addition of the straight lines 72, 84, and 85, the negative branchof straight line (shown by dots) having to be suppressed. The additionof the straight lines 72 and 84 is effected in the same manner as hasbeen described in FIG. 8 in connection with straight lines 72 and 73. Inaddition an equation j (below) of the straight line 85 has to be added.For the equation h the factor r 0.5, for equation i the factor K 0.1 andequationj receives the factor K 0.12. These values are divided on theordinate.

The equation for the straight line 85 is as follows:

- (j) For this it is necessary that its value from K (H2 at Ax 0 takesoff with an increasing Ax until, at Ax= 0.5Ay, the value nil isobtained. With further increasing Ax values the sign changes until at Axl the value he comes C K This negative (shown in dots) branch is not tobe used.

The straight line 85 therefore intersects the ordinate at Ax 0.5Ay= 0.5.The knee of the polygonal path is located above this point. The knee isgiven by the equation:

Z=|Ax Ayl/Ax Ay In the case of our example it should be located at Ax1/2 Ay,

For the practical execution of the operation by electronic means it isadvantageous to transform the equation k as follows:

IAx Ayl- Z(Ax Ay) 0,

receiving the equation of the straight line 85 intersecting the zeroline in the knee Ax l/2 Ay. Only the left hand positive branch locatedabove the zero line is to be used. The right hand branch (not used)having a negative value is blocked in electronically by a diode.

FIG. shows an electronic circuit arrangement which implements theimproved approximation method explained with reference to FIG. 9. Theadders 74, 75, the rectifier 79, as well as the summing device 77 andthe correcting device 61 are understood from FIG. 8. The equations ofadditional lines are to be added to the sum A B which is formed in theadding device 77. The polygonal path of the approximation curve consistsof the total sum of the equations of the additional lines and the sum AB. These equations are C, C, C,,. Firstly, we satisfy ourselves with C;that means an approximation according to FIG. 9 having only one knee.The factors calculated and assumed from the drawing (FIG. 9) are:

r 0.5; K, 0.1; K =0.12 and Z=1/3 The terms of a sum r,(Ax Ay) and K,| AxAylare available at lines 76 and 80 as electric potentials. Acorresponding voltage passes through the voltage divider 86, which formsthe factor Z/K,, to the second negative input of the subtractor 88, atwhose first input the unipolar voltage I A): Ayl is applied, via theline 80. The resultant voltage on the line 89 can be positive ornegative. However, only the positive value is to be used correspondingto the left hand positive branch of the straight line 85 in FIG. 9. Thenegative voltage is blocked by means of the blocking diode 90. Thepositive voltage passes over line 91 to the summing device 77. The sumvoltage on the line 60 subsequently passes through the correcting member61 and controls in a known manner the beam current from the cathode raytube. Deflection of the beam occurs at always the same times by means ofthe deflecting amplifiers 63 and 64, as already described.

The circuit may be developed to achieve ever greater precision, in anydesired fashion. At each knee at which the polygonal path increased, thenumber of aggregates 86, 88 and 90 is increased by one. The factors K,K, and also the values for Z, Z are advantageously determinedgraphically. In addition, a drawing is to be prepared which must beextended logically with respect ill to FIG. 9. The individual lineportions of the polygonal path are extended up to the intersection pointwith the ordinate. The lengths divided up on the ordinate, result incorresponding scale in the values K... The projections of the knees tothe abscissa give the values for Z....

Two modifications of the embodiments according to the invention will nowbe described. If the differences between the points become too large, itis advantageous to change the adjustment values, namely the recordingspeed and the associated beam brightness according to FIGS. 2 and 5, orthe recording time and the beam current according to the circuits ofFIGS. 6 and 10 in matched stages; criteria for these inversions are thedifference voltages 8x and By.

A predetermined beam speed and beam current is adjusted in the firstease up to a fixed limit value 5x or 8y. If one of the values 8x or Byor both exceed this limit at greater point distances, the saw-toothgenerators l5 and 16 in FIG. 2 or 44 and 45 in FIG. 5 and in additionthe beam current control 25 in FIG. 5 are switched over to the nextfixed operational range. It is also possible to extend this switchingover to more than only two ranges.

In the second case which is implemented by the circuit arrangement inFIGS. 6 and 8 and 10, swtiching over effects upon exceeding the distancelimit that the intervals between the startand stop-pulses from thetiming pulse generator become larger, so that with larger pointspacings, the recording time is not dispor portionally small and thebeam current is not too great. In addition, the difference voltagevalues 8x 8y at the input terminals 1 and 2 are reduced by one factor orif more operational ranges are desired, selectively by additionalfactors. The time intervals supplied by the generator 65 are increasedby the same factor.

However, the switching over of the operational range within one thesedescribed methods is only one of the possible modifications. Cases canbe conceived in which it is advantageous, dependent of the pointspacings between which the line member is to be plotted, to change thearrangement or even the method. Very large line pieces areadvantageously plotted at constant speed, whilst with short piecesconstant recording time is at least preferable.

Although we have described our invention by reference to specificexamples, many changes and modifications of the invention may be made byone skilled in the art without departing from the true spirit and scopeof the invention, and it is to be understood that we intent to includewithin the patent warranted on this invention all such changes andmodifications as may reasonably and properly be included within thescope of our contribution to the art.

We claim:

1. Apparatus for recording line drawings on the screen of a CRT whichhas horizontal and vertical dcflection circuits, a horizontal and avertical deflection coil, a recording beam emission circuit, the linedrawings represented by a plurality of individually spaced coordinatepoints, each line drawing recorded by the recording beam connecting aninitial coordinate point and an end coordinate point, means to producedeflection voltages representing the initial coordinate point, means toproduce deflection voltages for connecting the initial coordinate pointwith the end coordinate point, and means to produce difference voltagesrepresenting the difference between initial coordinate point and the endcoordinate point comprising:

adding means for adding thedeflection voltages to the deflection coils,said adding means connected between the deflection coils and the meansto produce the deflection voltages which represent the initialcoordinate point and the means to produce the deflection voltages forconnecting the individual coordinate point with the end coordinatepoint,

sawtooth generating means producing constant slope sawtooth voltageswhich represent the deflection voltages for connecting the initialcoordinate point and the end coordinate point, said slope beingdependent upon the difference voltages derived from the initialcoordinate point and the end coordinate point of the line drawing,comparator means having an output and a pair of inputs for receivingrespective horizontal and vertical difference signals and operable toprovide a first signal at its said output when the horizontal differencevoltage is less than the vertical difference voltage and a second signalat its said output when the horizontal difference voltage is greaterthan the vertical difference voltage, dividing amplifier means having apair of inputs and an output and operable to provide at its said outputthe quotient of the voltage on a first of said pair of inputs divided bythe voltage on a second of said pair of inputs,

first switching means having a first input for receiving the horizontaldifference voltages and a second input for receiving the verticaldifference voltage, a pair of outputs connected to said pair of inputsof said dividing amplifier means, and a control input connected to saidoutput of said comparator means and operable in response to said firstand second signals to selectively connect said horizontal and verticaldifference voltages to the input of said dividing amplifier means, and

second switching means having a pair of inputs for receiving saidsawtooth voltages, a pair of outputs connected to said deflectioncircuits and a control input connected to said comparator means andoperable in responseto'said first and second signals to selectivelyconnect said horizontal and vertical sawtooth voltages to the horizontaland vertical deflection circuits.

2. Apparatus according to claim 1, comprising function amplifier meansconnected between said output of said dividing means and said saw-toothvoltage generating means for selectively operating said sawtoothgenerating means in accordance with sin are 1 and cos arc lg functions.

3. Apparatus according to claim 1 comprising means for dividing saiddifference voltages by one another to provide quotients that are lessthan unity and means for forming sin arc tg and cos arc tg functionsfrom said quotients, and wherein said sawtooth generator means islinearly responsive to said sin arc tg and cos arc lg functions tocontrol the deflection circuits.

4. Apparatus for recording line drawings on a screen of a CRT which hashorizontal and vertical deflection circuits, a horizontal and a verticaldeflection coil, a recording beam emission circuit, the line drawingsrepresented by a plurality of individually spaced coordinate points,each line drawing recorded by the recording beam connecting an initialcoordinate point and an end coordinate point, means to producedeflection voltages representing the initial coordinate point, means toproduce deflection voltages for connecting the initial coordinate pointto the end coordinate point, and means to produce difference voltagesrepresenting the difference between the initial coordinate point and theend coordinate point comprising:

adding means for adding the deflection voltages to the deflection coils,said adding means connected between the deflection coils and the meansto produce the deflection voltages which represent the initialcoordinate point and themeans to produce the deflection voltages forconnecting the individual coordinate point with the end coordinatepoint, sawtooth generating means producing constant slope sawtoothvoltages which represent the deflection voltages for connecting theinitial coordinate point and the end coordinate point, said slope beingdependent upon the difference voltages derived from the initialcoordinate point and the end coordinate point of the line drawing, atiming pulse generator for producing repetitive pulses, said sawtoothgenerating means including timing pulse input connections connected tosaid timing pulse generator, said sawtooth generating means beingresponsive to successive timing pulses to turn on and off, means forcontrolling beam current of the CRT including means for squaring saiddifference voltages, means for adding the squared voltages, means forextracting the square root of the added square voltages, and means fordistoring the square root voltage connected to the recording beamemission circuit, means for adding the difference voltages, means forsubtracting the difference voltages including means for rendering thesubtraction effective without regard to sign, means for adding the sumand difference of said difference voltages connected to said means fordistorting for distortion of said difference voltages. 5. Apparatusaccording to claim 4 comprising at least one voltage divider connectedto the output of said means for adding the difference voltages, a secondmeans for subtracting connected to the first mentioned means forsubtracting and to said voltage divider for subtracting to provide theabsolute value difference between the voltages provided by said voltagedivider and said first-mentioned means for subtracting, said secondmeans for subtracting also connected to said means for adding the sumand difference of said difference voltages.

6. Apparatus for recording line drawings on the screen of a CRT whichhas horizontal and vertical deflection circuits, a horizontal and avertical deflection coil, a recording beam emission circuit, the linedrawings represented by a plurality of individually spaced coordinatepoints, each line drawing recorded by the recording beam connecting aninitial coordinate point and an end coordinate point, means to producedeflection voltages representing the initial coordinate point, means toproduce deflection voltages for connecting the initial coordinate pointwith the end coordinate point, and means to produce difference voltagesrepresenting the difference between the initial coordinate point and theend coordinate point comprising:

adding means for adding the deflection voltages to the deflection coils,said adding means connected between the deflection coils and the meansto produce the deflection voltages which represent the initialcoordinate point and the means to produce the deflection voltages forconnecting the initial coordinate point with the end coordinate point,

sawtooth generating means producing constant slope sawtooth voltageswhich represent the deflection voltages for connecting the initialcoordinate point to the end coordinate point, said slope being dependentupon the difference voltages derived from the initial coordinate pointand the end coordinate point of the line drawing,

two variable gain amplifier means each having an input forsimultaneously receiving the difference voltages, a control input, andan output connected to said sawtooth generators,

two function amplifiers, each of said function ampli fiers including aninput connected to the output of one of said variable gain amplifiermeans, said function amplifiers operable to square the output voltagesof said variable gain amplifier means,

an adjustable voltage source representing the desired value of thedrawing speed of the recording beam between adjacent points of thedrawing, and

an adder circuit including an output connected to said gain controlinputs of said variable gain ampli-

1. Apparatus for recording line drawings on the screen of a CRT whichhas horizontal and vertical deflection circuits, a horizontal and avertical deflection coil, a recording beam emission circuit, the linedrawings represented by a plurality of individually spaced coordinatepoints, each line drawing recorded by the recording beam connecting aninitial coordinate point and an end coordinate point, means to producedeflection voltages representing the initial coordinate point, means toproduce deflection voltages for connecting the initial coordinate pointwith the end coordinate point, and means to produce difference voltagesrepresenting the difference between initial coordinate point and the endcoordinate point comprising: adding means for adding the deflectionvoltages to the deflection coils, said adding means connected betweenthe deflection coils and the means to produce the deflection voltageswhich represent the initial coordinate point and the means to producethe deflection voltages for connecting the individual coordinate pointwith the end coordinate point, sawtooth generating means producingconstant slope sawtooth voltages which represent the deflection voltagesfor connecting the initial coordinate point and the end coordinatepoint, said slope being dependent upon the difference voltages derivedfrom the initial coordinate point and the end coordinate point of theline drawing, comparator means having an output and a pair of inputs forreceiving respective horizontal and vertical difference signals andoperable to provide a first signal at its said output when thehorizontal difference voltage is less than the vertical differencevoltage and a second signal at its said output when the horizontaldifference voltage is greater than the vertical difference voltage,dividing amplifier means having a pair of inputs and an output andoperable to provide at its said output the quotient of the voltage on afirst of said pair of inputs divided by the voltage on a second of saidpair of inputs, first switching means having a first input for receivingthe horizontal difference voltages and a second input for receiving thevertical difference voltage, a pair of outputs connected to said pair ofinputs of said dividing amplifier means, and a control input connectedto said output of said comparator means and operable in response to saidfirst and second signals to selectively connect said horizontal andvertical difference voltages to the input of said dividing amplifiermeans, and second switching means having a pair of inputs for receivingsaid sawtooth voltages, a pair of outputs connected to said deflectioncircuits and a control input connected to said comparator means andoperable in response to said first and second signals to selectivelyconnect said horizontal and vertical sawtooth voltages to the horizontaland vertical deflection circuits.
 2. Apparatus according to claim 1,comprising function amplifier means connected between said output ofsaid dividing means and said saw-tooth voltage generating means forselectively operating said sawtooth generating means in accordance withsin arc tg and cos arc tg functions.
 3. Apparatus according to claim 1comprising means for dividing said difference voltages by one another toprovide quotients that are less than unity and means for forming sin arctg and cos arc tg functions from said quotients, and wherein saidsawtooth generator means is linearly responsive to said sin arc tg andcos arc tg functions to control the deflection circuits.
 4. Apparatusfor recording line drawings on a screen of a CRT which has horizontaland vertical deflection circuits, a horizontal and a vertical deflectioncoil, a recording beam emission circuit, the line drawings representedby a plurality of individually spaced coordinate points, each linedrawing recorded by the recording beam connecting an initial coordinatepoint and an end coordinate point, means to produce deflection voltagesrepresenting the initial coordinate point, means to produce deflectionvoltages for connecting the initial coordinate point to the endcoordinate point, and means to prOduce difference voltages representingthe difference between the initial coordinate point and the endcoordinate point comprising: adding means for adding the deflectionvoltages to the deflection coils, said adding means connected betweenthe deflection coils and the means to produce the deflection voltageswhich represent the initial coordinate point and the means to producethe deflection voltages for connecting the individual coordinate pointwith the end coordinate point, sawtooth generating means producingconstant slope sawtooth voltages which represent the deflection voltagesfor connecting the initial coordinate point and the end coordinatepoint, said slope being dependent upon the difference voltages derivedfrom the initial coordinate point and the end coordinate point of theline drawing, a timing pulse generator for producing repetitive pulses,said sawtooth generating means including timing pulse input connectionsconnected to said timing pulse generator, said sawtooth generating meansbeing responsive to successive timing pulses to turn on and off, meansfor controlling beam current of the CRT including means for squaringsaid difference voltages, means for adding the squared voltages, meansfor extracting the square root of the added square voltages, and meansfor distoring the square root voltage connected to the recording beamemission circuit, means for adding the difference voltages, means forsubtracting the difference voltages including means for rendering thesubtraction effective without regard to sign, means for adding the sumand difference of said difference voltages connected to said means fordistorting for distortion of said difference voltages.
 5. Apparatusaccording to claim 4 comprising at least one voltage divider connectedto the output of said means for adding the difference voltages, a secondmeans for subtracting connected to the first mentioned means forsubtracting and to said voltage divider for subtracting to provide theabsolute value difference between the voltages provided by said voltagedivider and said first-mentioned means for subtracting, said secondmeans for subtracting also connected to said means for adding the sumand difference of said difference voltages.
 6. Apparatus for recordingline drawings on the screen of a CRT which has horizontal and verticaldeflection circuits, a horizontal and a vertical deflection coil, arecording beam emission circuit, the line drawings represented by aplurality of individually spaced coordinate points, each line drawingrecorded by the recording beam connecting an initial coordinate pointand an end coordinate point, means to produce deflection voltagesrepresenting the initial coordinate point, means to produce deflectionvoltages for connecting the initial coordinate point with the endcoordinate point, and means to produce difference voltages representingthe difference between the initial coordinate point and the endcoordinate point comprising: adding means for adding the deflectionvoltages to the deflection coils, said adding means connected betweenthe deflection coils and the means to produce the deflection voltageswhich represent the initial coordinate point and the means to producethe deflection voltages for connecting the initial coordinate point withthe end coordinate point, sawtooth generating means producing constantslope sawtooth voltages which represent the deflection voltages forconnecting the initial coordinate point to the end coordinate point,said slope being dependent upon the difference voltages derived from theinitial coordinate point and the end coordinate point of the linedrawing, two variable gain amplifier means each having an input forsimultaneously receiving the difference voltages, a control input, andan output connected to said sawtooth generators, two functionamplifiers, each of said function amplifiers including an inputconnected to the output of one of said variable gain amplifier meAns,said function amplifiers operable to square the output voltages of saidvariable gain amplifier means, an adjustable voltage source representingthe desired value of the drawing speed of the recording beam betweenadjacent points of the drawing, and an adder circuit including an outputconnected to said gain control inputs of said variable gain amplifiermeans, and a plurality of inputs connected to said adjustable voltagesource and said outputs of said function amplifier means for adding saidsquared output voltages and comparing such voltages with the voltage ofsaid adjustable voltage source to provide control voltages to saidvariable gain amplifier means, whereby said variable gain amplifiermeans regulates the slope of a sawtooth voltage of said sawtoothgenerating means for each difference voltage with respect to bothdifference voltages and the voltage of the adjustable voltage source.